Title Projectives in subcategories of category O
Abstract: We will discuss the construction of sufficiently many projective objects in certain subcategories of category O for Kac-Moody Lie algebras, and related categories, and some of the consequences. The ideas are due to Bernstein, Gelfand and Gelfand, Rocha-Caridi and Wallach, Soergel, and Andersen, Jantzen and Soergel.